Bulletin géodésique

, Volume 65, Issue 2, pp 92–101 | Cite as

The geodetic approximations in the conversion of geoid height to gravity anomaly by Fourier transform

  • Brian Farelly


Six sources of error in the use of Fourier methods for the conversion of geoid heights to gravity anomalies are considered. The errors due to spherical approximation are unimportant. The errors due to approximations in Stokes' integral may be eliminated by use of the gravity coating rather than the gravity anomaly. The chord-to-arc error and the truncation error may be reduced by using a reference field. Tapering of the edges of the measurement window reduces the truncation error. The long-wavelength components of the high degree spherical harmonics cause small offsets in the resulting gravity anomalies. The errors due to the plane approximation can be reduced by appropriate choice of map projection and area of integration.


Gravity Anomaly Truncation Error Fourier Method Geoid Height Gravity Disturbance 
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  1. Bracewell RN (1986) The Fourier transform and its applications, 2nd edn., revised. McGraw-Hill, New York.Google Scholar
  2. Colombo OL (1981) Numerical methods for harmonic analysis on the sphere. Report no. 310, Dept. of Geodetic Science and Surveying, The Ohio State University.Google Scholar
  3. Forsberg R, Kearsley AHW (1990) Precise gravimetric geoid computations over large regions in: Brunner FK, Rizos C (eds), Developments in Four-Dimensional Geodesy. Springer Verlag, pp 65–82.Google Scholar
  4. Heiskanen WA, Moritz H (1967) Physical Geodesy. W.H.Freeman and Company.Google Scholar
  5. Jordan SK (1978) Fourier physical geodesy. Report No. AFGL-TR-78-0056, The Analytic Sciences Corp., Reading, Massachusetts.Google Scholar
  6. MacRobert TM (1967) Spherical Harmonics, 3rd edn. Pergamon Press.Google Scholar
  7. Molodenskii MS, Yeremeyev VF, Yourkina MI (1962) Methods for the study of the external gravitational field and figure of the earth, transl. from Russian (1960). Israel program for scientific translations, Jerusalem.Google Scholar
  8. Moritz H (1980) Advanced Physical Geodesy. Herbert Wichmann Verlag/-Abacus Press.Google Scholar
  9. Press WH, Flannery BP, Teukolsky SA, Vetterling WT (1986) Numerical recipes. Cambridge University Press.Google Scholar
  10. Schwarz KP, Sideris MG, Forsberg R (1990) The use of FFT techniques in physical geodesy. Geophys.J.Int. vol 100, pp 485–514.CrossRefGoogle Scholar
  11. Sideris MG (1987) On the application of spectral techniques to the gravimetric problem. Proc. XIX IUGG General Assembly, Vancouver, B.C, Aug. 9–22, Tome II, pp 428–442.Google Scholar
  12. Sjøberg LE (1989) Refined least squares modification of Stokes' formula in: Andersen OB (ed) Modern Techniques in Geodesy and Surveying. National Survey and Cadastre, Denmark, pp 365–379.Google Scholar
  13. Strang van Hees GL (1990) Contribution to geoid computation with FFT methods. Paper presented at 1st International Geoid Commission Symposium, Milan.Google Scholar
  14. Wong L, Gore R (1969) Accuracy of geoid heights from modified Stokes' kernels. Geophys.J.R.Astr.Soc. vol 18 pp 81–91.Google Scholar
  15. Zucker PA (1990) Smoothing and desmoothing in the Fourier approach to spherical coefficient determination. Int.Symposium on Kinematic Systems in Geodesy, Surveying and Remote Sensing, Banff, Canada 10–13 Sep., proceedings in print.Google Scholar

Copyright information

© Springer-Verlag 1991

Authors and Affiliations

  • Brian Farelly
    • 1
  1. 1.Norsk Hydro Research CentreBergenNorway

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